Unexpected Probability

Sorry for not blogging all week, but this trend will probably continue for the rest of the term as workload is not-so-gradually increased.

Anyway, most readers are probably aware of the simple "birthday problem" from high school: given that there are 365 days in a year, and that every birthdate is equally likely, what is the probably that in a group of n people, at least 2 share the same birthday? (Same month/day, ignoring year)

Naturally, the answer is 1 - 365^(n)/(365^n) (or 1 - (365Pn)/365^n)), which is very close to 1 even if n is of moderate size (say about 40). However, in real life, the probability that two persons share the same birthday is often found to be much lower; for example, most people in a class have unique birthdates.

Yesterday the statistics professor performed the following experiment in our (relatively small) class:
One by one, each individual announces his/her birthdates. If another person in the class has that birthdate as well, then that person announces the fact, and the process terminates.

Well, the process terminated at the first person. The disbelieving professor demanded proof, which both individuals provided via their student card/driver's license. Unsatisfied, the professor continued the procedure (skipping the paired students). Again, the process terminated after he asked one person. Again, the professor demanded proof, which both individuals produced. Now, what is the probability of that? Heh. Since the class was laughing so hard (we couldn't help it...), the professor gave up after that.

On a more mundane note, I still have to complete the following:

• Physics*2 (first to practice, second to hand in)
• Linear algebra (3 more problems to go...currently stuck. Also, need to confirm the format of one problem with the professor tomorrow)
• Statistics, before I get buried alive in the deluge of nontrivial probability/statistical problems. (That'd be a terrible fate, and the course is set up so that this situation happens Very easily.)
• Calculus, which I haven't looked at yet though I really, really should. (And the first bonus problem is there, already!) Ugh, I still don't understand uniform continuity...better work on that, too.
  
• Begin Thermodynamics assignment 2. At least I sort of finished the first Organic Chemistry problem set...
• Review intermolecular bonding and crystal structure, which should not take too long but still requires time.
• Write 5 cover letters to totally different jobs and converting them to HTML format, look for more available positions, and somehow find someone who has known me for more than 5 years and is willing to write me a reference letter. Sadly, the last part is the most challenging, which is not a positive indicator of my social capabilities. Oh well, having a life is always secondary to doing something actually enjoyable, right?
• Prepare for chemistry lab, beginning next Tuesday. Although the reaction is straightforward, I hope it will go well!
• If I don't get my course enrollment automatically straightened out by the end of this month (when the Registrar has no more excuses to delay the issue), I'll have to go chase after my advisor and the faculty committee. That'd be no fun.
• Chores, like laundry. Disclaimer: I should point out that I actually use the washing machine regularly, unlike certain university students that can be named.
  
• Practicing the piano, which qualify more as a "slacking" mechanism than a task to be completed
  

Of course, the reams of homework never end...CS assignment 2 is available beginning tomorrow. And I just finished assignment 1 yesterday, too. Oh well. With a box of timbits (half of which is already consumed) by my side as motivator, I should finish my physics sometime tonight/early "tomorrow".

Of course, that doesn't explain the open window on my computer showing a performance of the Intermezzo Op. 118 No. 2 by Brahms, nor the blinking MSN conversation...(I think I am undergoing a "Brahms phase"...practicing the Brahms Rhapsodies is on my list of things-to-accomplish as well.)